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 Llibres Llibres 101 - 110 de 188 sobre C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides.... C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of ... - Pàgina 66
per Jeremiah Day - 1815 - 126 pàgines
Visualització completa - Sobre aquest llibre ## A Treatise on Plane and Spherical Trigonometry

1863 - 256 pàgines
...proposition is therefore general in its application.* 118. The »urn of any two side» of a plane triangle ie to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. For, by the preceding article, a : b =»...
Visualització completa - Sobre aquest llibre ## Elements of Plane Trigonometry: And Their Application to the Measurement of ...

1864
...the first proportion in Theorem I. THEOREM III. 41. In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference. Let ABC be a triangle ; then AB + BC:BC—...
Visualització completa - Sobre aquest llibre ## McGill University Calendar, and Examination Papers

1865
...latter formula, determine tan. 15°, first finding tan. 30°. 5. The sum of the two sides of a triangle is to their difference as the tangent of half the sum of the base angles is to the tangent of half the difference. 6. Prove that if A" be the number of seconds...
Visualització completa - Sobre aquest llibre ## Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair, Euclid - 1855 - 317 pàgines
...the 3d. Let ABC be a triangle ; the sum of AB and AC any two sides, is to the difference of AB and AC as the tangent of half the sum of the angles ACB and ABC, to the tangent »f half their difference. About the centre A with the radius AB, the greater of the two sides, d«•cribe...
Visualització completa - Sobre aquest llibre James Pryde - 1867 - 458 pàgines
...the sides a and b and also subtract them, this will give a + b and a — b/ then the sum of the sides is to their difference as the tangent of half the sum of the remaining angles to the tangent of half their difference. The half sum and half difference being added,...
Visualització completa - Sobre aquest llibre ## Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - 1867 - 283 pàgines
...sin. B : cos. (AB) ....... (44) THEOREM in. (ART. 9.) In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the ai,(/lei opposite to^them is to the tangent of half then- difference. „ . a sin. A , (Theorem 2.)...
Visualització completa - Sobre aquest llibre ## A TREATISE ON LAND-SURVEYING: COMPRISING THE THEORY DEVELOPED FROM THE ...

...to each other as the opposite sides. THEOREM II. — In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III.— In every plane triangle,...
Visualització completa - Sobre aquest llibre ## Elements of Trigonometry: Plane and Spherical

Lefébure de Fourcy (M., Louis Etienne) - 1868 - 288 pàgines
...tang } (A + B) a — b tang} (A — B) *• ; which shows that, in any triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite to those sides is to the tangent of half their difference. We have A + B=180° — C; hence...
Visualització completa - Sobre aquest llibre ## Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - 1868 - 420 pàgines
...BA-cos. A. That is, b = a cos. C -J- e cos. A. 869. Theorem — The sum of any two sid.es of a triangle is to their difference as the tangent of half the sum of the two opposite angles is to the tangent of half their difference. By Art. 867, a : b : : sin. A : sin....
Visualització completa - Sobre aquest llibre ## A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - 1869 - 428 pàgines
...to each other at the opposite sides. THEOREM EL — In every plane triangle, the turn of two tides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every plane triangle,...
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